Trivia

Subject:
Another way to look at it
Response To:
Re: Nearly there ()

Alex Y
At each stage, the previous balance is multiplied by 1.5 and an amount is pulled out of the bag. Chronologically, it happens in the opposite order, which is needed so that D doesn't pull out and distribute pennies to E and C before passing the bag to A. But mathematically, it can be looked at in this order.

A's original N into the bag gets increased 4 times, by C, E, B, and D, so its contribution to the final amount in the bag is
N*1.5^4 = (5 1/16)*N
C's withdrawal of 6 gets increased 3 times, so its contribution to the final amount is
-6*1.5^3 = -(3 3/8)*6 = -20 1/4
Other withdrawals have analogous effects on the total:
E: -5*1.5^2 = -(2 1/4)*5 = -11 1/4
B: -4*1.5 = -6
D: -8
A: +2

So the final amount in the bag is
(5 1/16)N - 20 1/4 - 11/1/4 - 6 - 8 + 2
=(5 1/16)N - 43 1/2
Set this equal to 5N and solve to get
(1/16) N = 43 1/2, or
N = 16 * (43 1/2) = 696

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